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Quantum Physics

Title:A Blueprint for a Topologically Fault-tolerant Quantum Computer

Abstract: The advancement of information processing into the realm of quantum mechanics
promises a transcendence in computational power that will enable problems to be
solved which are completely beyond the known abilities of any "classical"
computer, including any potential non-quantum technologies the future may
bring. However, the fragility of quantum states poses a challenging obstacle
for realization of a fault-tolerant quantum computer. The topological approach
to quantum computation proposes to surmount this obstacle by using special
physical systems -- non-Abelian topologically ordered phases of matter -- that
would provide intrinsic fault-tolerance at the hardware level. The so-called
"Ising-type" non-Abelian topological order is likely to be physically realized
in a number of systems, but it can only provide a universal gate set (a
requisite for quantum computation) if one has the ability to perform certain
dynamical topology-changing operations on the system. Until now, practical
methods of implementing these operations were unknown. Here we show how the
necessary operations can be physically implemented for Ising-type systems
realized in the recently proposed superconductor-semiconductor and
superconductor-topological insulator heterostructures. Furthermore, we specify
routines employing these methods to generate a computationally universal gate
set. We are consequently able to provide a schematic blueprint for a fully
topologically-protected Ising based quantum computer using currently available
materials and techniques. This may serve as a starting point for attempts to
construct a fault-tolerant quantum computer, which will have applications to
cryptanalysis, drug design, efficient simulation of quantum many-body systems,
solution of large systems of linear equations, searching large databases,
engineering future quantum computers, and -- most importantly -- those
applications which no one in our classical era has the prescience to foresee.